Radian Measure Gamma maths chapter33 radians to degrees, degrees to radians, angle and sector area

Calculate the area of the dark part of his circle. The radius is 12.5 m long. 368.16 m2 (1dp)

Two sectors have the same centre angle 1 radian = the angle formed in a sector with the arc length the same as the radius 1 radian The length of an arc is proportional to both: The angle at the centre of the arc The radius of the arc Two sectors have the same radius Two sectors have the same centre angle Θ s θ 3s r 3r Θ s 2θ 2s

Arc Length Formula s = rθ s s = arc length r = length of radius Θ = angle at centre of sector, measured in radians θ r r Rearranging the arc length formula, we have: angle = arc length or θ = s radius r

Conversion of degrees/radians 00 3600 2π π 1800 3600 = 2 π so 1800 = π To convert degrees to radians, multiply by To convert radians to degrees, multiply by

Convert 450 to radians. Leave your answer in terms of π 450 = 45 x = x π = x π = Convert radians to degrees. Answer = 2 x 180 = 360 = 1200 3 3 Using the arc length formula calculate the length of the arc ABC s = rθ so ABC = rθ = 8 x = cm or in decimal form 20.1 cm (1dp) B A 8 cm C 8 cm

Calculate the size of the angle labelled θ in degrees.   6 5 θ 5

Sector area formula Area A = ½ r2 θ (note θ is in radians) Answer Π The angle at the centre of the shaded sector is 2π - = Area of sector = ½ x 22 x = cm2 or 10.47 cm2 (4sf) Π 3 2 cm 2 cm The sector area formula can be rearranged to make either θ or r the subject 2A = r2θ Θ = r =

Area of Segment Your calculator must be set in radians The Area of a Segment is the area of a sector minus the triangular piece. Your calculator must be set in radians Area of Segment = ½ × (θ - sin θ) × r2 = ½ × ( (θ × π/180) - sin θ) × r2   (if θ is in degrees)